Luminosity distance in "Swiss cheese" cosmology with randomized voids: I. Single void size

TL;DR

This paper investigates how inhomogeneities in Swiss cheese cosmological models affect supernova luminosity distances, demonstrating that proper randomization diminishes the apparent acceleration effects previously attributed to voids.

Contribution

It shows that the apparent acceleration in Swiss cheese models is due to insufficient randomization and can be mitigated with proper void placement, challenging claims that voids alone explain supernova data.

Findings

Proper randomization reduces the effect of voids on luminosity distances.

Weak gravitational lensing explains the apparent acceleration effects.

Insufficient randomization can lead to exaggerated demagnification effects.

Abstract

Recently there have been suggestions that the Type Ia supernova data can be explained using only general relativity and cold dark matter with no dark energy. In "Swiss cheese" models of the Universe, the standard Friedmann-Robertson-Walker picture is modified by the introduction of mass compensating spherical inhomogeneities, typically described by the Lemaitre-Tolman-Bondi metric. If these inhomogeneities correspond to underdense cores surrounded by mass-compensating overdense shells, then they can modify the luminosity distance-redshift relation in a way that can mimic accelerated expansion. It has been argued that this effect could be large enough to explain the supernova data without introducing dark energy or modified gravity. We show that the large apparent acceleration seen in some models can be explained in terms of standard weak field gravitational lensing together with insufficient randomization of void locations. The underdense regions focus the light less than the homogeneous background, thus dimming supernovae in a way that can mimic the effects of acceleration. With insufficient randomization of the spatial location of the voids and of the lines of sight, coherent defocusing can lead to anomalously large demagnification effects. We show that a proper randomization of the voids and lines of sight reduces the effect to the point that it can no longer explain the supernova data.